During the illumination of a luminescent body with primary light, the different refractive index of the luminescent body compared to air can lead to partial reflection of the primary radiation on the luminescent material surface, which can be calculated according to Fresnel's equations. In order to suppress this Fresnel reflection, an antireflection layer may be applied onto the luminescent material surface. This is often impractical, however, since for example the material of the luminescent body surface does not allow long-lasting application of an antireflection layer. It is also known for the primary radiation to shine first through a transparent carrier for the luminescent body and only then onto the luminescent body. The side of the carrier facing away from the luminescent body may then be provided with an antireflection layer. A disadvantage in this case is that Fresnel reflections can also occur at the interface between the carrier and the luminescent body, and furthermore that the carrier can have an absorbing effect for the primary radiation.